Median Radial Basis Functions Neural Network Adrian G. BorYsand

     


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1 X(1)

Y1

2

X(2)

Y2

YM

X(N)

L INPUT

HIDDEN LAYER

8.


’G»

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OUTPUT

0.08 p 2

0.07 0.06

p 3 0.05

p 1

0.04 0.03 0.02 0.01 0 0

2

4

T1 6

8

8.
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10 T2

12

14

16

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0.02 0 0

2

4

6

8

10

8.
XN!›

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12

14

16

-0.02

Median

Expected bias of the location parameter

-0.04 -0.06 -0.08 -0.1 -0.12 -0.14 -0.16 -0.18

Mean

-0.2 -0.22

0

20

40

60

80

100

120

140

160

180

200

140

160

180

200

No. samples

Y.
/mrk?@ „A

0.1

Expected bias of the scale parameter

0.05 0 -0.05 MAD

-0.1 -0.15 -0.2 -0.25 -0.3

Sample standard deviation 0

20

40

60

80

100 No. samples

8.
mr?S#pA 8.
mr›

’ r

120

Bias in center estimation

-0.5 -- mean -1 - median -1.5 1

2 3 Scale parameter (a)

4

0

Bias in scale estimation

Bias in center estimation Bias in scale estimation

0

-0.5

-1

-- classical - MAD

-1.5 1

2 3 Scale parameter (c)

4

8.
Xx!›

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0.8 0.6 0.4

-- mean

0.2

- median

0 1

2 3 Scale parameter (b)

4

0

-1 -- classical

-2

- MAD -3

1

2 3 Scale parameter (d)

4

20

15

6 

10

FEATURE II

. . ... . . .. .. . . . . ... .. . ... ... . . . . . . . . . .. .. . . .. . .. .. . . . . . . . .. . . ... . . ... . . . . . . ...... .... ..... .... . . . . . . .. . . .. ... . .. . . . . . . . . . . . . . . . . . . . .. . .. . . .... . . . . .... . . ... . ..... ......... ........... ......... .... . .. .. ........... ... .. .... .. ..... .. .... . ...... . . . . . . .. . . . . . . . .. . . .. . . . .. .... ...... ... ... . . ... .... ...... .. .. ... ...... .... . .. ... .. .. .. .. . . . . .. . .... .. ..... . .... ..... .. .......... ..... ........ .. .... .... ..... . ........ . . . . . .. .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. ... .. .. . . . . ... . ........ .. . . . . .. .. . . . ... . . . . . . ... . ..................... ........ .. . ........ ........... .... ... ..... ... .. .. .... . . . ..... ... . . ... . ... . . ... .. .. .... . . .. . . . . .. .... .... ... .. .. . . . . . . . ... ... . .. . . .. ... ... . ............ . .. ......... ... .. .... ........ . . . .. . . . . . ... . . ... ... ..... . . .. .. .. ... . . . . . . . ... . . ... .. ........ .... ..... ........ ........ . ....... ... ... . .. .......... .. .......... . . .. . . . . . . .. . . . . . . . ........ ....... ........... ... ... ......... . . .. .... .... .. . .. .... . . ... . ..... . . . .. . .. .... . ........... ... ... ..... .......... ..... ............ ..... ... ......................... .. ... . . . . . .. . ...... .... ... .... .. ......... .. ...... .. . ..... . .. ... ............................ ... .. . . . . . . . . . . .. ..... ... . . . . . . . . .. .. .. . . . . ... . .. . . . ...... .. . .. ... .. . . .. .. . . . . . . .... . . . . . . . . .. .... . . . . . . .

5

.. .

.

0

.

. . . . . .. .. .

6E 

6E 

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.

6 

.

.

.

-10 -10

-5

0

5 FEATURE I

8.
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10

15

20

20 .

15

6 

FEATURE II

10

5

0 .

-5

. .. . . . .. . . . . .. . .... ..... .. . . . . . ..... . ... . . ..... . . . . . .... ..... ... . .. . . . . .. .. . .. . . . . . . . . . . . . . . ............. ........ .. . . . . . . . . . . . . .. ...... .... .. . . . .. .... . . .. . . . .... . . . .. . ..... ... ........................ ........ . . . .. .. . ... .... ... .. ... ...... .. . ... ... . .. .... . .......... .... ...... .... . ...... ... .. . . .... ... .. .. .. . . ... . . . .. . . .. .... ............... ..... . . . .. . .. . .. ........ ....... .... ... .. ...... ... . . . ... . . . . .. .... ............................................. .. ...... .. .. .... ............... .. ................................ ......... ... . . . . . . . . . . ......... .................................................. ........... ... .......... ... .............................................. ... ... ...... . ... ... . . .... ........................................ ....... .... . . .......... ....... ............... . ................................................. ................ ... . .. .... . . . . . ................ ................. .. .. . . .... .. .. ........................................... .. .................... . ... . ... .. .. . .. . . . . . . . ........ ............................... ... .. . ... . .. ....... ... .............. ....... ..... ... .. ... ...... .. . . . .. . ....... ................................ . . . . . .... ............... .... ........ .. ............ ......... .. . ... . . . . . . . . . . ..... . .. . . . . . . . . . . . .. . . .. . . . . . . . . . .. . ... .......................... ..... ... . ....... . . .. ... ....... .. . ... ......... .. . .... .. . ... . . ..... .... ....... . . . . . . ... . . ......... ..... .. .. .. .... .... . ... .. . . .. . .. . . . . . . . . ... . .. . .. . ..... ....... ... .... . ........ .. . .... .. .. .............. ... . ...... . . .. . .. . . . . . . . .. . ............................. ........................................................................................... ..................... ....... ............ ... .. .. . ..... . . .. . . . . . .. .... .. ... .. ......... ................ .... .. ................... ....................................... ... ...... ............................................ .... . ..... . .... . . . ... ....... ... . ....... . . . . ... .... . .. .. .................. .. ... .... ..... ......... ..... . .. . ... . .... . . . . . . . . . . . . . ..... . . ... ......... .............. . ... . ............ . .. .... .. .......... ... ...... .... .. .. ......... .... . .... . ..... .... . . . .. . . ... .. . . . .. ... . . . .. . . . . ... ... . . . . . . . . . . . . . . . . .. .. . . .. . ...

6E 

. .

. .

. .

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-5

.

0

5 FEATURE I

8.
U†E›

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10

15

20

25

Mean Square Error

20

15

RBF - Euclidean

10 MRBF - Euclidean RBF - Mahalanobis 5 MRBF - Mahalanobis 0

0

500

1000

1500

2000 Data samples

8.
XŠ!›

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2500

3000

3500

4000

Y.
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